CN103017728A - Method for determining direction vector of antenna array in interference environment - Google Patents

Abstract

The invention discloses a method for determining a direction vector of an antenna array and belongs to the field of electronic information technologies. The method comprises the steps of carrying out initialization processing, establishing a sample autocorrelation matrix for received signal vectors, determining noise subspaces and signal subspaces in current and all discrete directions, establishing noise subspace correlated matrixes and determining the minimum singular value of all the matrixes, obtaining an angle difference between an interference signal direction and a test signal source direction, and determining the direction vector of the antenna array. According to the method, on the basis that the antenna array receives signal vector samples, a constraint relation that a first element of the noise subspaces, signal subspaces, noise subspace correlated matrixes, signal subspace correlated matrixes and direction vector of the sample autocorrelation matrix is equal to 1 is adopted, and then, the determination of the direction vector of the antenna array in an interference environment is realized. The method has the characteristics that correlation coefficients between the determined direction vector and an actual direction vector are all higher than 97%, 95% of the correlation coefficients are higher than 99%, the similarity is very high, and the like.

Description

The assay method of aerial array direction vector under the interference environment

Technical field

The invention belongs to the assay method of the aerial array direction vector in the electronic information technical field, particularly a kind of assay method of the aerial array direction vector under interference environment.

Background technology

More and more higher along with the detection of spatial domain signal and parameter estimation are required, process as the antenna array signals of spatial processing Main Means and to be widely used in the numerous areas such as electronic reconnaissance, radar, communication, sonar, earthquake, radio astronomy.Aerial array has the outstanding advantages such as signal gain height, wave beam control is flexible, spatial resolution is high, for many years constantly is subject to domestic and international researcher and pays close attention to.Yet, no matter be the beam scanning aerial array in World War II later stage, or current digital antenna array or the intelligent antenna array of moving communicating field, the error of aerial array is always ubiquitous, causes the direction vector of aerial array very large with the result difference that adopts theoretical analytic formula to calculate.The corresponding different aerial array direction vector of each direction, it is accurately known in advance that existing high-resolution direction finding technology all requires the aerial array direction vector, when having larger error between the aerial array direction vector of known aerial array direction vector and reality, inevitably can cause the Measure direction performance degradation of aerial array.Therefore, obtaining accurately, the aerial array direction vector is study hotspot and the difficult point of antenna array signals process field always, can be bring into play the prerequisite that antenna array signals is processed many advantages, also be to restrict one of key factor that can the antenna array signals treatment technology practical.

Existing aerial array direction vector assay method is at first with discrete--direction, then will test to be placed on the discrete direction with signal source and transmit, aerial array is determined the mean value of the received signal vector of aerial array by repeatedly receiving this signal, and with the mean value of this aerial array received signal vector as the aerial array direction vector.But, the prerequisite that adopts this aerial array direction vector assay method is not have undesired signal in the supposition working environment, otherwise, when aerial array is determined the received signal vector of aerial array by receiving signal, not only comprise test the transmitting with signal source on the discrete direction that is placed on setting in the received signal vector of aerial array, also comprise the undesired signal from other direction, and the direction of undesired signal is unknown in advance.At this moment, if will adopt the measured aerial array direction vector of the method as the received signal vector of this aerial array this moment, its result will cause between gained aerial array direction vector and the actual aerial array direction vector and have larger error, thereby causes the defectives such as Measure direction performance degradation of aerial array.

Summary of the invention

The objective of the invention is the problem for the background technology existence, research and develop the assay method of aerial array direction vector under a kind of interference environment, with from the aerial array received signal vector that contains undesired signal that measures, reject its undesired signal, recover direction that test transmits with signal source the direction vector of corresponding array antenna, and then provide accurately the purpose such as parameter for the direction finding of aerial array.

Solution of the present invention is on the expression basis of the aerial array received signal vector sample of background technology, for the received signal vector of aerial array and the test problem with the disturbed signal corruption of one-to-one relationship between the corresponding array antenna direction vector of sense of signal source emission, the noise subspace of the sample autocorrelation matrix of the received signal vector of employing aerial array, signal subspace, correlated noise subspace matrix, first element of correlation signal subspace matrix and direction vector equals the restriction relation such as 1, realizes recovering test with the corresponding array antenna direction vector of sense of signal source emission from the received signal vector of the aerial array that is interfered.

The sample of the received signal vector of the aerial array that the present invention adopts is typically expressed as:

x(t,θ _k)=a(θ _k)s ₁(t)+a(θ _k+η)s ₂(t)+v(t)

X (t, θ wherein _k) be the received signal vector of aerial array, vectorial dimension equals the antenna number M of aerial array, and t is sampling instant, s ₁(t), s ₂(t) and v (t) to be respectively test vectorial with the receiver noise of the transmitting of signal source, undesired signal and aerial array, θ _kFor test uses signal source with respect to the direction of aerial array, namely need measure the discrete direction of aerial array direction vector, k=1,2,, K, K are the number that needs the corresponding discrete direction of aerial array direction vector of mensuration, η is the direction of undesired signal and tests with the differential seat angle between the direction of signal source, a (θ _k) and a (θ _k+ η) be respectively test with the direction θ of signal source _kCorresponding aerial array direction vector and the direction θ of undesired signal _kThe aerial array direction vector that+η is corresponding.

Because the test direction θ of signal source _kCorresponding aerial array direction vector a (θ _k) and test the s emission signal s of using signal source ₁(t) multiply each other together, fuzzy for avoiding amplitude, be without loss of generality, all suppose a (θ _k) first element equal 1.

When the signal that does not exist undesired signal and test with the signal source emission is better than the receiver noise of aerial array far away, received signal vector x (t, the θ of aerial array _k) approximate a (θ _k) s ₁(t), therefore can measure the direction θ that signal source is used in test _kCorresponding aerial array direction vector a (θ _k) be vector x (t, θ _k) divided by vector x (t, θ _k) first element; And the aerial array direction vector a (θ that determines by this way _k) first element equal 1.

But, when having undesired signal, received signal vector x (t, the θ of aerial array _k) equal to test the direction θ with signal source _kCorresponding aerial array direction vector a (θ _k) and the direction θ of undesired signal _kThe aerial array direction vector a (θ that+η is corresponding _k+ η) linear combination, therefore, can not be again with vector x (t, θ _k) divided by vector x (t, θ _k) first element as test with the direction θ of signal source _kCorresponding aerial array direction vector a (θ _k), otherwise will cause aerial array obvious angle measurement error in the practical application of direction finding, to occur, even can't obtain the direction finding result.

The sample autocorrelation matrix of the used aerial array received signal vector of the inventive method is:

$R\left({\mathrm{\θ}}_k\right)=\frac{1}{T}\underset{t=1}{\overset{T}{\mathrm{\Σ}}}x(t,{\mathrm{\θ}}_k)x^H(t,{\mathrm{\θ}}_k)$

R (θ wherein _k) represent to test with signal source at direction θ _kSample autocorrelation matrix when transmitting, ∑ represent summation, and t is sampling instant, and each sampling instant samples to a received signal vector, t=1 then, and 2 ..., T, T represent the number of the aerial array received signal vector corresponding with the sampling instant number, [] ^HThe conjugate transpose of expression vector or matrix.

Test uses signal source at direction θ _kWhen transmitting, the svd of sample autocorrelation matrix is:

R(θ _k)=U(θ _k)Λ(θ _k)U ^H(θ _k)

Matrix Λ (θ wherein _k) be diagonal matrix, the element that the diagonal angle makes progress is corresponding sample autocorrelation matrix R (θ respectively _k) singular value, be λ by descending sort ₁(θ _k) 〉=λ ₂(θ _k) λ ₃(θ _k) 〉=... 〉=λ _M(θ _k), matrix U (θ _k) be by sample autocorrelation matrix R (θ _k) singular vector u ₁(θ _k), u ₂(θ _k), u ₃(θ _k) ..., u _M(θ _k) matrix that consists of, corresponding one by one with singular value, [] ^HThe conjugate transpose of expression vector or matrix.

Test uses signal source at direction θ _kWhen transmitting, the noise subspace of the sample autocorrelation matrix of aerial array is:

Q _n(θ _k)=[u ₃(θ _k) u ₄(θ _k) … u _M(θ _k)]

The signal subspace of the sample autocorrelation matrix of aerial array is:

Q _s(θ _k)=[u ₁(θ _k) u ₂(θ _k)]

The present invention namely utilizes first element of noise subspace, signal subspace and direction vector of sample autocorrelation matrix of the received signal vector of aerial array to equal the restriction relation such as 1, from the received signal vector of the aerial array that is interfered, recover thus test with the array antenna direction vector corresponding to sense of signal source emission, thereby realize its goal of the invention.Thereby the inventive method comprises:

Step 1. initialization process: with the antenna number of receiving antenna array, the number and all discrete directions that need the corresponding discrete direction of aerial array direction vector of mensuration, received signal vector number on each discrete direction, test deposits internal memory with the setting party of signal source in to initialization

Step 2. is set up the sample autocorrelation matrix of received signal vector: at first with aerial array over against test with the setting party of signal source to or the 1st discrete direction receive test with the signal of signal source, and process signal vector to determine that aerial array receives through conventional method, then set up the sample autocorrelation matrix of received signal vector;

Step 3. is determined noise subspace and the signal subspace on the current direction: sample autocorrelation matrix is carried out its svd, determine noise subspace and the signal subspace of sample autocorrelation matrix;

Step 4: determine signal subspace and noise subspace on all discrete directions: aerial array is gone to next discrete direction and receives signal and the repeating step 2,3 that signal source is used in test, thereby determine signal subspace and noise subspace on this discrete direction; Then determine successively as stated above signal subspace and noise subspace on all discrete directions;

Step 5. is set up correlated noise subspace matrix and is determined each subspace Smallest Singular Value of Matrices: at first utilize noise subspace and the noise subspace on the another one discrete direction on first discrete direction to set up correlated noise subspace matrix, and to this correlated noise subspace matrix carry out svd, with definite minimum singular value; Set up respectively noise subspace on first discrete direction and the correlated noise subspace matrix of the noise subspace on all the other each (respectively) discrete directions by above method, and determine the minimum singular value of each correlated noise subspace matrix, turn step 6;

Step 6. is obtained the undesired signal direction and is tested with the differential seat angle between the signal source direction: at first the minimum singular value of the whole correlated noises of step 5 gained subspace matrix is searched for, finding out minimum value wherein, the gained minimum value is the minimum singular value in the minimum singular value of whole correlated noises subspace matrix; Discrete direction angle corresponding to this minimum singular value is the deflection of undesired signal, after then determining to be somebody's turn to do (undesired signal) deflection and testing the differential seat angle of using between the signal source direction angle, turns step 7;

The mensuration of step 7. aerial array direction vector: at first with the direction of measurement of arbitrary discrete direction as the aerial array direction vector, utilize the signal subspace on this arbitrary discrete direction and set up correlation signal subspace matrix apart from the differential seat angle of this discrete direction for the signal subspace on another discrete direction of step 6 gained differential seat angle, then the restriction relation of utilizing first element of direction vector to equal 1, thus measure aerial array direction vector on this arbitrary discrete direction; Aerial array direction vector on last according to said method sequentially determining all the other each discrete directions except above-mentioned arbitrary discrete direction is namely finished the mensuration to aerial array direction vector under the interference environment.

Sample at the received signal vector of aerial array described in the step 2 is typically expressed as:

x(t,θ _k)=a(θ _k)s ₁(t)+a(θ _k+η)s ₂(t)+v(t)

Wherein: x (t, θ _k) be the received signal vector of aerial array, vectorial dimension equals the antenna number M of aerial array, and t is sampling instant, s ₁(t), s ₂(t) and v (t) to be respectively test vectorial with the receiver noise of the transmitting of signal source, undesired signal and aerial array, θ _kBe direction, the k=1 of test with signal source, 2 ..., K, K are the number of discrete direction, η is the direction of undesired signal and tests with the differential seat angle between the signal source direction, a (θ _k), a (θ _k+ η) be respectively test with the direction θ of signal source _kCorresponding aerial array direction vector and the direction θ of undesired signal _kThe aerial array direction vector that+η is corresponding, and a (θ _k) first element equal 1.

And at the sample autocorrelation matrix of the received signal vector of aerial array described in the step 2 be:

$R\left({\mathrm{\θ}}_k\right)=\frac{1}{T}\underset{t=1}{\overset{T}{\mathrm{\Σ}}}x(t,{\mathrm{\θ}}_k)x^H(t,{\mathrm{\θ}}_k)$

Wherein, R (θ _k) represent to test with signal source at direction θ _kSample autocorrelation matrix when transmitting, ∑ represent summation, and t is sampling instant, and each sampling instant samples to a received signal vector, t=1 then, and 2 ..., T, T represent the number of the aerial array received signal vector corresponding with the sampling instant number, [] ^HThe conjugate transpose of expression vector or matrix.

Processing to determine the signal vector of aerial array reception through conventional method described in the step 2, its disposal route is I/Q dual channel receiver method or Hilbert transform disposal route.

Described in the step 3 sample autocorrelation matrix is being carried out its svd, the svd of sample autocorrelation matrix is:

R(θ _k)=U(θ _k)Λ(θ _k)U ^H(θ _k)

Wherein: matrix Λ (θ _k) be diagonal matrix, the element on the diagonal line is corresponding sample autocorrelation matrix R (θ respectively _k) singular value, be λ by descending sort ₁(θ _k) 〉=λ ₂(θ _k) λ ₃(θ _k) 〉=... 〉=λ _M(θ _k), matrix U (θ _k) be by sample autocorrelation matrix R (θ _k) singular vector u ₁(θ _k), u ₂(θ _k), u ₃(θ _k) ..., u _M(θ _k) matrix that consists of, corresponding one by one with singular value, [] ^HThe conjugate transpose of expression vector or matrix.

Determine noise subspace and the signal subspace of sample autocorrelation matrix described in the step 3, wherein:

The noise subspace of sample autocorrelation matrix is:

Q _n(θ _k)=[u ₃(θ _k) u ₄(θ _k) … u _M(θ _k)]

The signal subspace of sample autocorrelation matrix is:

Q _s(θ _k)=[u ₁(θ _k) u ₂(θ _k)]

In above-mentioned two formulas: u ₁(θ _k), u ₂(θ _k), u ₃(θ _k) ..., u _M(θ _k) sample autocorrelation matrix R (θ _k) in singular vector, corresponding one by one with singular value, k=1,2 ..., K, K are the number of discrete direction, M is the number of antenna in the aerial array.

Utilize noise subspace on first discrete direction and the noise subspace on the another one discrete direction to set up correlated noise subspace matrix described in the step 5 to be:

$G\left({\mathrm{\θ}}_k\right)={\left[\begin{array}{c}{Q}_n\left(0\right)\\ Q_n\left({\mathrm{\θ}}_k\right)\end{array}\right]}^H\left[\begin{array}{c}{Q}_n\left(0\right)\\ Q_n\left({\mathrm{\θ}}_k\right)\end{array}\right]$

Wherein: Q _n(θ _k) for testing with signal source at direction θ _kThe signal subspace of the sample autocorrelation matrix of aerial array and noise subspace when transmitting, k=2,3 ..., 360;

Described in the step 5 this correlated noise subspace matrix being carried out svd is:

G(θ _k)=W(θ _k)Ω(θ _k)W ^H(θ _k)

Wherein: matrix Ω (θ _k) be diagonal matrix, the element that the diagonal angle makes progress is corresponding correlated noise subspace matrix G (θ respectively _f) singular value, be β by descending sort ₁(θ _k) 〉=β ₂(θ _k) β ₃(θ _k) 〉=... 〉=β _M-2(θ _k), minimum singular value is β _M-2(θ _k), k=2 wherein, 3 ..., 360, matrix W (θ _f) be by correlated noise subspace matrix G (θ _f) the matrix that consists of of singular vector, corresponding one by one with singular value, W ^H(θ _k) be W (θ _f) associate matrix;

Setting up correlation signal subspace matrix described in the step 7 be:

$D\left({\mathrm{\θ}}_k\right)=\left[\begin{array}{c}{q}_s\left({\mathrm{\θ}}_k\right)\\ q_s\left({\mathrm{\θ}}_{k+k_0-1}\right)Q_s^H\left({\mathrm{\θ}}_{k+k_0-1}\right)Q_s\left({\mathrm{\θ}}_k\right)\end{array}\right]$

Q wherein _s(θ _k) and

Be respectively signal subspace Q _s(θ _k) and

The first row vector, Q _s(θ _k) with Being respectively test uses signal source at direction θ _kWith

The signal subspace of the sample autocorrelation matrix of aerial array when transmitting,

Be

Conjugate transpose, k=1,2 ..., 360, k ₀Be the definite β of step 6 _M-2(θ _k) k value corresponding to minimum singular value.

Equaling 1 restriction relation at first element that utilizes direction vector described in the step 7 is:

$D\left({\mathrm{\θ}}_k\right)g\left({\mathrm{\θ}}_k\right)=\left[\begin{array}{c}1\\ 1\end{array}\right]$

Aerial array direction vector on arbitrary discrete direction of measuring is:

b(θ _k)=Q _s(θ _k)g(θ _k)

Wherein: g (θ _k) expression discrete direction θ _kOn the coordinate coefficient of aerial array direction vector in signal subspace, equaled 1 restriction relation by first element of direction vector and be defined as:

$g\left({\mathrm{\θ}}_k\right)=D^{-1}\left({\mathrm{\θ}}_k\right)\left[\begin{array}{c}1\\ 1\end{array}\right]$

More than various in: b (θ _k) be discrete direction θ _kThe measurement result of upper aerial array direction vector, Q _s(θ _k) for testing with signal source at direction θ _kThe signal subspace of the sample autocorrelation matrix of aerial array when transmitting, D ^-1(θ _k) expression correlation signal subspace matrix D (θ _k) contrary.

The present invention is because on the basis of the aerial array received signal vector sample of background technology, adopt first element of noise subspace, signal subspace, correlated noise subspace matrix, correlation signal subspace matrix and direction vector of sample autocorrelation matrix of the received signal vector of aerial array to equal the restriction relation such as 1, thereby realize from the received signal vector of the aerial array that is interfered, recovering test with the corresponding array antenna direction vector of sense of signal source emission.Through correlation test, adopt related coefficient between direction vector that the inventive method records and the corresponding actual direction vector all greater than 97%, and the direction vector that records at 95% discrete direction and the related coefficient between the actual direction vector be all greater than 99%, and the direction vector that the correlativity between itself and the actual direction vector is measured on the 90% above direction of background technology and the related coefficient between the actual direction vector are all less than 90%.Thereby the present invention has the impact that the electromagnetic interference (EMI) that can effectively eliminate in the environment is measured the array antenna direction vector of measuring, error between measured aerial array direction vector and the actual aerial array direction vector is little, similarity is high, is subjected to the characteristics such as the impact of ambient electromagnetic field undesired signal is little in the mensuration process.

Description of drawings

Fig. 1 is for adopting instantiation mode of the present invention in the minimum singular value that has correlated noise subspace matrix corresponding to different angles in the situation of undesired signal, and ordinate is minimum singular value, is designated as β _M-2(θ _k), horizontal ordinate is direction θ _k=k-1 degree, k=2 ..., 360.

Fig. 2 is for adopting instantiation mode of the present invention having the direction vector measured in the situation of undesired signal and the related coefficient between the actual direction vector, and ordinate is related coefficient, is designated as ρ (θ _k), horizontal ordinate is direction θ _k=k-1 degree, k=1,2 ..., 360.

Embodiment

Present embodiment take radius as 2 times of wavelength, the uniform circular array that forms of 9 antennas is as example, i.e. M=9; The received signal vector number T=48 that needs the aerial array of reception; Discrete direction θ is set in this example _k=k-1, k=1,2 ..., 360, namely need the number K=360 of the corresponding discrete direction of the aerial array direction vector measured.Test is set is located at 0 degree direction with signal source, signal to noise ratio (S/N ratio) is 13dB; The undesired signal direction is unknown, is set to 32.2 degree in this example, and the receiver signal to noise ratio (S/N ratio) is 16dB; Uniform circular array is placed on the turntable, and the control turntable rotates with the interval of 1 degree, turn to respectively 0 degree, 1 degree ..., 359 degree, be equivalent to changing test with the direction of signal source with respect to aerial array; Turntable moves in the direction of the clock, and every rotation 1 degree all will receive signal by aerial array, determines 48 received signal vectors of this antenna capable of adjusting angle array.

The flow process of the specific embodiment of the present invention is as follows:

Step 1. initialization process: with the antenna number (9) of receiving antenna array, need number (360) and all discrete direction θ of the corresponding discrete direction of aerial array direction vector of mensuration _k=k-1, k=1,2 ..., 360, received signal vector number on each discrete direction (48), test deposits internal memory with the setting party of signal source in to (0 degree) initialization;

Step 2. is set up the sample autocorrelation matrix of received signal vector: at first with aerial array over against test with the setting party of signal source to or the 1st discrete direction (θ ₁=0 degree) receives the signal that signal source is used in test, then adopt this area disposal route I/Q dual channel receiver method (or Hilbert transform disposal route) commonly used to determine the signal vector x (t that aerial array receives, 0), t is sampling instant, and each sampling instant is sampled to a received signal vector, and present embodiment is t=1 then, 2,, 48, then set up the sample autocorrelation matrix of received signal vector:

$R\left(0\right)=\frac{1}{48}\underset{t=1}{\overset{48}{\mathrm{\Σ}}}x(t,0)x^H(t,0)$

Wherein, ∑ represents summation, and t is sampling instant, [] ^HThe conjugate transpose of expression vector or matrix;

Step 3. pair sample autocorrelation matrix carries out its svd:

R(0)=U(0)Λ(0)U ^H(0)

Wherein: matrix Λ (0) is diagonal matrix, the element that the diagonal angle makes progress is the singular value of corresponding sample autocorrelation matrix R (0) respectively, pressing descending sort is 1.2124 〉=0.4863〉0.0071 〉=0.0061 〉=0.0053 〉=0.0040 〉=0.0033 〉=0.0028 〉=0.0021, and matrix U (0) is the singular vector u by sample autocorrelation matrix R (0) ₁(0), u ₂(0), u ₃(0) ..., u ₉(0) matrix that consists of is corresponding one by one with singular value; Note Q _s(0) and Q _n(0) being respectively test uses signal source at direction θ ₁=0 spends signal subspace and the noise subspace of the sample autocorrelation matrix of aerial array when transmitting, and determines the signal subspace of sample autocorrelation matrix:

$Q_s\left(0\right)=\left[\begin{array}{cc}{u}_1\left(0\right)& u_2\left(0\right)\end{array}\right]$

$=\left[\begin{array}{cc}-0.3442+0.0000i& 0.3666+0.0000i\\ 0.0556-0.1184i& -0.4924+0.2269i\\ 0.3863+0.0787i& 0.1315+0.0583i\\ -0.0419-0.3350i& -0.0235-0.2852i\\ -0.2710-0.1907i& 0.3221+0.2558i\\ 0.0253-0.4068i& 0.0702-0.0017i\\ 0.1081-0.1747i& 0.1517-0.4410i\\ 0.4064-0.0860i& -0.0280+0.0726i\\ -0.0403+0.3205i& -0.0422+0.2641i\end{array}\right]$

And noise subspace:

$Q_n\left(0\right)=\left[\begin{array}{cccc}{u}_3\left(0\right)& u_4\left(0\right)& \·\·\·& u_9\left(0\right)\end{array}\right]$

$=\left[\begin{array}{ccccccc}-0.4071-0.0000i& 0.2990-0.0000i& -0.4089+0.0000i& 0.2269-0.0000i& -0.1766+0.0000i& -0.4794-0.0000i& 0.1106+0.0000i\\ -0.0962+0.2386i& 0.3207-0.1160i& -0.1841+0.1922i& 0.1531-0.2395i& 0.1854-0.0127i& 0.1268-0.2317i& 0.4346+0.2484i\\ -0.4339+0.1768i& -0.1463-0.1185i& 0.3809-0.0171i& -0.0210-0.1826i& -0.3881-0.2674i& -0.1014-0.1228i& -0.0429+0.3748i\\ 0.4426+0.0441i& 0.2269+0.0421i& 0.3228+0.2706i& 0.2910-0.0553i& -0.0104-0.0815i& -0.4095-0.1767i& -0.2314+0.1691i\\ -0.1821+0.2764i& 0.0397+0.0719i& 0.3628-0.0155i& 0.1094+0.1669i& 0.5031+0.0391i& 0.1686+0.2813i& -0.0375+0.2637i\\ -0.0551-0.1880i& 0.1144+0.1501i& 0.0559+0.2797i& 0.2309+0.0239i& -0.4125-0.2453i& 0.4150+0.3573i& 0.2067-0.2164i\\ -0.2091-0.2525i& 0.2853-0.2433i& 0.1423+0.1283i& -0.5019+0.2318i& 0.2186-0.0095i& 0.0201-0.1433i& 0.2847+0.0089i\\ -0.0746+0.1054i& 0.5364-0.0888i& 0.0615-0.4240i& 0.0564-0.1716i& 0.1496-0.0701i& -0.0567+0.1866i& -0.2619-0.3987i\\ 0.2557+0.1152i& 0.4623-0.1151i& 0.0722+0.0211i& -0.1358+0.5439i& -0.3772+0.0552i& 0.0714+0.0685i& -0.0415+0.2043i\end{array}\right]$

Step 4: rotary antenna array extremely next discrete direction also receives the signal that signal source is used in test, repeating step 2,3, thereby signal subspace and noise subspace on definite this discrete direction; Determine signal subspace and noise subspace on all discrete directions by above method, namely 0 degree, 1 degree, 2 degree ..., the signal subspace Q on the 359 degree directions _s(0), Q _s(1), Q _s(2) ..., Q _s(359) and noise subspace Q _n(0), Q _n(1), Q _n(2) ..., Q _n(359);

Step 5. utilizes noise subspace and the noise subspace on the another one discrete direction on first discrete direction to set up correlated noise subspace matrix, that is:

$G\left({\mathrm{\θ}}_k\right)={\left[\begin{array}{c}{Q}_n\left(0\right)\\ Q_n\left({\mathrm{\θ}}_k\right)\end{array}\right]}^H\left[\begin{array}{c}{Q}_n\left(0\right)\\ Q_n\left({\mathrm{\θ}}_k\right)\end{array}\right]$

Wherein: Q _n(θ _k) for testing with signal source at direction θ _kThe signal subspace of the sample autocorrelation matrix of aerial array and noise subspace when transmitting, k=2,3 ..., 360, and correlated noise subspace matrix carried out svd:

G(θ _k)=W(θ _k)Ω(θ _k)W ^H(θ _k)

Wherein: matrix Ω (θ _k) be diagonal matrix, the element that the diagonal angle makes progress is corresponding correlated noise subspace matrix G (θ respectively _f) singular value, be β by descending sort ₁(θ _k) 〉=β ₂(θ _k) β ₃(θ _k) 〉=... 〉=β _M-2(θ _k), matrix W (θ _f) be by correlated noise subspace matrix G (θ _f) the matrix that consists of of singular vector, corresponding one by one with singular value; Determine that minimum singular value is β _M-2(θ _k) (concrete value is seen Fig. 1); Set up respectively noise subspace on first discrete direction and the correlated noise subspace matrix of the noise subspace on all the other each discrete directions by above method, determine that then the minimum singular value of each correlated noise subspace matrix is β _M-2(θ _k), k=2,3 ..., 360, turn step 6;

Step 6. at first searches for minimum value in all correlated noise subspace Smallest Singular Value of Matrices, is minimum singular value, and searches for k=2 by the mode that increases progressively, 4 ..., 360, determine β _M-2(θ _k) k corresponding to minimum singular value be k ₀Then determine discrete direction corresponding to this minimum singular value, this discrete direction θ _K0Be the deflection of undesired signal, the deflection of then determining this undesired signal is poor with first discrete direction angle, and this difference is the direction and the differential seat angle of testing between the usefulness direction of signal source of undesired signal; As seen from Figure 1, β _M-2(θ _k) k corresponding to minimum singular value be k ₀=33, corresponding differential seat angle is 32 degree;

Step 7. is for a discrete direction θ _k, determine another one with it angle differ the discrete direction that equals the differential seat angle that step 6 determines

On signal subspace

With for this discrete direction θ _kOn signal subspace Q _s(θ _k) jointly set up together correlation signal subspace matrix:

$D\left({\mathrm{\θ}}_k\right)=\left[\begin{array}{c}{q}_s\left({\mathrm{\θ}}_k\right)\\ q_s\left({\mathrm{\θ}}_{k+k_0-1}\right)Q_s^H\left({\mathrm{\θ}}_{k+k_0-1}\right)Q_s\left({\mathrm{\θ}}_k\right)\end{array}\right]$

Q wherein _s(θ _k) and

Be respectively signal subspace Q _s(θ _k) and

The first row vector, Q _s(θ _k) with

Being respectively test uses signal source at direction θ _kWith

The signal subspace of the sample autocorrelation matrix of aerial array when transmitting, k=1,2 ..., 360, k ₀Be the definite minimum singular value β of step 6 _M-2(θ _k) k corresponding to minimum singular value; Then, utilize first element of direction vector to equal 1 restriction relation to be:

$D\left({\mathrm{\θ}}_k\right)g\left({\mathrm{\θ}}_k\right)=\left[\begin{array}{c}1\\ 1\end{array}\right]$

The aerial array direction vector of measuring on this discrete direction is:

b(θ _k)=Q _s(θ _k)g(θ _k)

B (θ wherein _k) be discrete direction θ _kThe measurement result of upper aerial array direction vector, g (θ _k) the coordinate coefficient of aerial array direction vector in signal subspace on this discrete direction of measuring of expression, g (θ _k) equal 1 restriction relation by first element of direction vector and be defined as:

$g\left({\mathrm{\θ}}_k\right)=D^{-1}\left({\mathrm{\θ}}_k\right)\left[\begin{array}{c}1\\ 1\end{array}\right]$

D ^-1(θ _k) expression correlation signal subspace matrix D (θ _k) contrary; Make k=1,2 ..., K determines the measurement result of aerial array direction vector on all discrete directions by above method, namely the final measurement result of aerial array direction vector is:

B=[b(θ ₁) b(θ ₂) … b(θ ₃₆₀)]。

Be the degree of approximation between check mensuration present embodiment gained direction vector and the actual direction vector, the related coefficient that defines between the two is ρ (θ _k), the direction vector that note is measured is b (θ _k), the actual direction vector is a (θ _k); Pass through following formula:

$\mathrm{\ρ}\left({\mathrm{\θ}}_k\right)=\frac{\left|a^H\left({\mathrm{\θ}}_k\right)b\left({\mathrm{\θ}}_k\right)\right|}{\sqrt{\left|a^H\left({\mathrm{\θ}}_k\right)a\left({\mathrm{\θ}}_k\right)\right|\left|b^H\left({\mathrm{\θ}}_k\right)b\left({\mathrm{\θ}}_k\right)\right|}}$

Check its approximate (be correlated with) degree and contrast with background technology, in the formula: [] ^HThe conjugate transpose of expression vector or matrix, || expression takes absolute value; Related coefficient is 100% near 1(more), the direction vector b (θ of then explanation mensuration _k) more near actual direction vector a (θ _k).

Fig. 2 is for adopting instantiation mode of the present invention having the direction vector measured in the situation of undesired signal and the related coefficient between the actual direction vector, and ordinate is correlation coefficient ρ (θ _k), horizontal ordinate is direction θ _k=k-1 degree, k=1,2 ..., 360.

Among the figure as seen, related coefficient between the direction vector of all mensuration and the corresponding actual direction vector is all greater than 97%, and in direction vector that 95% direction is measured and the related coefficient between the actual direction vector all greater than 99%, the direction vector and the vectorial no significant difference of actual direction measured are described.

In contrast, be the mean value of the received signal vector of corresponding aerial array if directly measure the aerial array direction vector of each direction, the direction vector of then measuring on the direction more than 90% and the related coefficient between the actual direction vector illustrate that all less than 90% the direction vector of measuring obviously departs from the actual direction vector.

Claims (10)

1. the assay method of aerial array direction vector under the interference environment comprises:

Step 1. initialization process: with the antenna number of receiving antenna array, the number and all discrete directions that need the corresponding discrete direction of aerial array direction vector of mensuration, received signal vector number on each discrete direction, test deposits internal memory with the setting party of signal source in to initialization;

Step 2. is set up the sample autocorrelation matrix of received signal vector: at first with aerial array over against test with the setting party of signal source to or the 1st discrete direction receive test with the signal of signal source, and process signal vector to determine that aerial array receives through conventional method, then set up the sample autocorrelation matrix of received signal vector;

Step 3. is determined noise subspace and the signal subspace on the current direction: sample autocorrelation matrix is carried out its svd, determine noise subspace and the signal subspace of sample autocorrelation matrix;

Step 4: determine signal subspace and noise subspace on all discrete directions: aerial array is gone to next discrete direction and receives signal and the repeating step 2,3 that signal source is used in test, thereby determine signal subspace and noise subspace on this discrete direction; Then determine successively as stated above signal subspace and noise subspace on all discrete directions;

Step 5. is set up correlated noise subspace matrix and is determined each correlated noise subspace Smallest Singular Value of Matrices: at first utilize noise subspace and the noise subspace on the another one discrete direction on first discrete direction to set up correlated noise subspace matrix, and to this correlated noise subspace matrix carry out svd, with definite minimum singular value; Set up respectively noise subspace on first discrete direction and the correlated noise subspace matrix of the noise subspace on all the other each discrete directions by above method, and determine the minimum singular value of each correlated noise subspace matrix, turn step 6;

Step 6. is obtained the undesired signal direction and is tested with the differential seat angle between the signal source direction: at first the minimum singular value of the whole correlated noises of step 5 gained subspace matrix is searched for, finding out minimum value wherein, the gained minimum value is the minimum singular value in the minimum singular value of whole correlated noises subspace matrix; Discrete direction angle corresponding to this minimum singular value is the deflection of undesired signal, after then determining this deflection and testing the differential seat angle of using between the signal source direction angle, turns step 7;

The mensuration of step 7. aerial array direction vector: at first with the direction of measurement of arbitrary discrete direction as the aerial array direction vector, utilize the signal subspace on this arbitrary discrete direction and set up correlation signal subspace matrix apart from the differential seat angle of this discrete direction for the signal subspace on another discrete direction of step 6 gained differential seat angle, then the restriction relation of utilizing first element of direction vector to equal 1, thus measure aerial array direction vector on this arbitrary discrete direction; Aerial array direction vector on last according to said method sequentially determining all the other each discrete directions except above-mentioned arbitrary discrete direction is namely finished the mensuration to aerial array direction vector under the interference environment.

2. by the assay method of aerial array direction vector under the described interference environment of claim 1, it is characterized in that at the sample of the received signal vector of aerial array described in the step 2 being:

x(t,θ _k)=a(θ _k)s ₁(t)+a(θ _k+η)s ₂(t)+v(t)

Wherein: x (t, θ _k) be the received signal vector of aerial array, vectorial dimension equals the antenna number M of aerial array, and t is sampling instant, s ₁(t), s ₂(t) and v (t) to be respectively test vectorial with the receiver noise of the transmitting of signal source, undesired signal and aerial array, θ _kBe direction, the k=1 of test with signal source, 2 ..., K, K are the number of discrete direction, η is the direction of undesired signal and tests with the differential seat angle between the signal source direction, a (θ _k), a (θ _k+ η) be respectively test with the direction θ of signal source _kCorresponding aerial array direction vector and the direction θ of undesired signal _kThe aerial array direction vector that+η is corresponding, and a (θ _k) first element equal 1.

3. by the assay method of aerial array direction vector under the described interference environment of claim 1, it is characterized in that at the sample autocorrelation matrix of the received signal vector of aerial array described in the step 2 being:

Wherein, R (θ _k) represent to test with signal source at direction θ _kSample autocorrelation matrix when transmitting, ∑ represent summation, and t is sampling instant, and each sampling instant samples to a received signal vector, t=1 then, and 2 ..., T, T represent the number of the aerial array received signal vector corresponding with the sampling instant number, [] ^HThe conjugate transpose of expression vector or matrix.

4. press the assay method of aerial array direction vector under the described interference environment of claim 1, it is characterized in that processing to determine the signal vector of aerial array reception through conventional method described in the step 2, its disposal route is I/Q dual channel receiver method or Hilbert transform disposal route.

5. by the assay method of aerial array direction vector under the described interference environment of claim 1, it is characterized in that in the svd of sample autocorrelation matrix described in the step 3 being:

R(θ _k)=U(θ _k)Λ(θ _k)U ^H(θ _k)

Wherein: matrix Λ (θ _k) be diagonal matrix, the element on the diagonal line is corresponding sample autocorrelation matrix R (θ respectively _k) singular value, be λ by descending sort ₁(θ _k) 〉=λ ₂(θ _k) λ ₃(θ _k) 〉=... 〉=λ _M(θ _k), matrix U (θ _k) be by sample autocorrelation matrix R (θ _k) singular vector u ₁(θ _k), u ₂(θ _k), u ₃(θ _k) ..., u _M(θ _k) matrix that consists of, θ _kBe the direction of test with signal source, k=1,2 ..., K, K are the number of discrete direction, [] ^HThe conjugate transpose of expression vector or matrix.

6. by the assay method of aerial array direction vector under the described interference environment of claim 1, it is characterized in that at noise subspace and the signal subspace of determining sample autocorrelation matrix described in the step 3, wherein:

The noise subspace of sample autocorrelation matrix is:

Q _n(θ _k)=[u ₃(θ _k) u ₄(θ _k) … u _M(θ _k)]

The signal subspace of sample autocorrelation matrix is:

Q _s(θ _k)=[u ₁(θ _k) u ₂(θ _k)]

In above-mentioned two formulas: u ₁(θ _k), u ₂(θ _k), u ₃(θ _k) ..., u _M(θ _k) sample autocorrelation matrix R (θ _k) in singular vector, θ _kBe the direction k=1 of test with signal source, 2 ..., K, K are the number of discrete direction, M is the number of antenna in the aerial array.

7. by the assay method of aerial array direction vector under the described interference environment of claim 1, it is characterized in that at the subspace of correlated noise described in the step 5 matrix being:

Wherein: Q _n(θ _k) for testing with signal source at direction θ _kThe signal subspace of the sample autocorrelation matrix of aerial array and noise subspace when transmitting, k=2,3 ..., 360.

8. by the assay method of aerial array direction vector under the described interference environment of claim 1, it is characterized in that in the svd of the subspace of correlated noise described in the step 5 matrix being:

G(θ _k)=W(θ _k)Ω(θ _k)W ^H(θ _k)

Wherein: matrix Ω (θ _k) be diagonal matrix, the element that the diagonal angle makes progress is corresponding correlated noise subspace matrix G (θ respectively _f) singular value, be β by descending sort ₁(θ _k) 〉=β ₂(θ _k) β ₃(θ _k) 〉=... 〉=β _M-2(θ _k), minimum singular value is β _M-2(θ _k), k=2 wherein, 3 ..., 360 matrix W (θ _f) be by correlated noise subspace matrix G (θ _f) the matrix that consists of of singular vector, W ^H(θ _k) be W (θ _f) associate matrix.

9. by the assay method of aerial array direction vector under the described interference environment of claim 1, it is characterized in that at the subspace of correlation signal described in the step 7 matrix being:

Wherein: q _s(θ _k) and

Be respectively signal subspace Q _s(θ _k) and

The first row vector, Q _s(θ _k) with

Being respectively test uses signal source at direction θ _kWith

The signal subspace of the sample autocorrelation matrix of aerial array when transmitting,

Be

Conjugate transpose, k=1,2 ..., 360, k ₀Be the definite β of step 6 _M-2(θ _k) k value corresponding to minimum singular value.

10. by the assay method of aerial array direction vector under the described interference environment of claim 1, it is characterized in that equaling 1 restriction relation at first element that utilizes direction vector described in the step 7 is:

Aerial array direction vector on arbitrary discrete direction of measuring is:

b(θ _k)=Q _s(θ _k)g(θ _k)

Wherein: g (θ _k) expression discrete direction θ _kOn the coordinate coefficient of aerial array direction vector in signal subspace, equaled 1 restriction relation by first element of direction vector and be defined as:

More than various in: b (θ _k) be discrete direction θ _kThe measurement result of upper aerial array direction vector, Q _s(θ _k) for testing with signal source at direction θ _kThe signal subspace of the sample autocorrelation matrix of aerial array when transmitting, D ^-1(θ _k) expression correlation signal subspace matrix D (θ _k) contrary.

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